Device and method for producing control data for the surgical correction of defective eye vision

ABSTRACT

A device for producing control data for a laser device for the surgical correction of defective vision. The device produces the control data such that the laser emits the laser radiation such that a volume in the cornea is isolated. The device calculates a radius of curvature R CV * to determine the control data, the cornea reduced by the volume having the radius of curvature R CV * and the radius of curvature being site-specific and satisfying the following equation: R CV *(r,φ)=1/((1/R CV (r,φ))+B COR (r,φ)/(n c -1))+F, wherein R CV (r,φ) is the local radius of curvature of the cornea before the volume is removed, n c  is the refractive index of the material of the cornea, F is a coefficient, and B COR (r,φ) is the local change in refractive force required for the desired correction of defective vision in a plane lying in the vertex of the cornea, and at least two radii r1 and r2 satisfy the equation B COR (r=r1,φ)≠B COR (r=r2,φ).

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of Application Ser. No. 13/145,759,filed Oct. 5, 2011, entitled “Device and Method for Producing ControlData for the Surgical Correction of Defective Eye Vision,” which in turnis a National Phase entry of PCT Application No. PCT/EP2010/050701,filed Jan. 21, 2010, which claims priority from German ApplicationNumber 102009005482.0, filed Jan. 21, 2009, each of which is herebyfully incorporated herein by reference.

TECHNICAL FIELD

In a first variant the invention relates to a device for generatingcontrol data for controlling a laser for the surgical correction of thedefective vision of an eye of a patient, wherein the control data areadapted to control a laser which cuts cornea tissue by irradiating laserradiation into the cornea of the eye, the device generates the controldata such that the laser, during operation according to the controldata, emits the laser radiation such that a volume in the cornea isisolated, the removal of which from the cornea effects the desiredcorrection of defective vision and, to determine the control data, thedevice calculates a radius of curvature that the cornea has when reducedby the volume.

In the first variant the invention further relates to a method forgenerating control data for controlling a laser for the surgicalcorrection of the defective vision of an eye of a patient, wherein thecontrol data are adapted to control a laser which cuts cornea tissue byirradiating laser radiation into the cornea of the eye, the control dataare generated such that the laser, during operation according to thecontrol data, emits the laser radiation such that a volume in the corneais isolated, the removal of which from the cornea effects the desiredcorrection of defective vision and, to determine the control data, aradius of curvature that the cornea has when reduced by the volume iscalculated.

In a second variant the invention relates to a method for generatingcontrol data which are adapted to control a laser for the surgicalcorrection of the defective vision of an eye of a patient, wherein,during operation of the laser, the cornea is deformed by pressing itsanterior surface against a contact surface, wherein in the method acorrection surface is predetermined for the non-deformed cornea, whichcorrection surface is to be generated for correction of defective visionas a cut surface in the cornea, and wherein, in the method, thedeformation of the cornea during operation of the laser is taken intoaccount by a transformation of the coordinates for points in thenon-deformed cornea into coordinates of the same points in the deformedcornea.

In a second variant the invention further relates to a device forgenerating control data which are adapted to control a laser for thesurgical correction of the defective vision of an eye of a patient,wherein, during operation of the laser, the cornea is deformed bypressing its anterior surface against a contact surface and wherein acorrection surface is predetermined for the non-deformed cornea, whichcorrection surface is to be generated for correction of defective visionas a cut surface in the cornea, and wherein the device, duringgenerating of the control data, takes into account the deformation ofthe cornea during operation of the laser by a transformation of thecoordinates for points in the non-deformed cornea into coordinates ofthe same points in the deformed cornea.

BACKGROUND

Spectacles are the traditional way of correcting defective vision in thehuman eye. However, refractive surgery which corrects defective visionby altering the cornea is now also increasingly being used. The aim ofthe surgical methods is to selectively alter the cornea so as toinfluence refraction. Differing procedures of surgeries are known forthis purpose. Currently the most widespread is the so-calledlaser-assisted in situ keratomileusis, also abbreviated to LASIK.Firstly, a lamella of the cornea is cut on one side from the corneasurface and folded to the side. This lamella can be cut by means of amechanical microkeratome or also by means of a so-called laser keratome,such as is marketed e.g. by Intralase Corp., Irvine, USA. After thelamella has been cut and folded to the side, the LASIK operation uses anexcimer laser, which removes the thus-exposed corneal tissue byablation. After volume in the cornea has been vaporized in this mannerthe lamella of the cornea is folded back into its original place.

The use of a laser keratome to expose the lamella is advantageous as thedanger of infection is thereby reduced and the cut quality increased. Inparticular the lamella can be produced with a very much more consistentthickness. The cut is also potentially smoother, which reduces sightproblems due to this boundary surface which remains even after theoperation.

To produce the cut, a series of incisions of the eye are made atpredetermined points such that the cut surface is formed as a result.With the laser keratome the cut surface forms the lamella to be foldedback before the use of laser ablation.

With the conventional LASIK method exposed corneal tissue is vaporized,which is also called “grinding” of the cornea by means of laserradiation. The volume removal which is necessary to correct defectivevision is set for each surface element of the exposed cornea by thenumber of laser pulses and their energy. Therefore, in the LASIK method,a so-called shot file is provided for the ablation laser which defines,for different points on the cornea, how often, and with what energy, thelaser beam is to be directed onto defined points on the cornea. Thevolume removal is heuristically determined, not least because it dependsgreatly on the ablation effect of the laser beam, therefore on thewavelength, fluence etc. of the radiation used. The state of the corneaalso plays a role; in particular the moisture content of the cornea isto be mentioned here. WO 96/11655 describes a device and a process forthe LASIK method. In particular a formula is given which calculates theradius of curvature to be achieved from the pre-operative radius ofcurvature of the cornea and the desired diopter correction. A similarcalculation is described in EP 1153584 A1—also for corneal ablation bymeans of LASIK.

U.S. Pat. No. 5,993,438 proposes the removal of a volume from the corneaby vaporization and absorption in the cornea.

WO 2005/092172 discloses how optical refraction power measurements whichhave been determined in one plane can be transferred into another plane.The document mentions that this process can be used for different eyetreatments, in particular for laser-supported ablation.

A further laser-based eye surgery method is not to vaporize the volumeto be removed from the cornea, but to isolate it by a laser cut. Thevolume is thus no longer ablated, but isolated in the cornea by athree-dimensional cut surface and thus made removable. Empirical valueswhich have been developed for grinding the cornea by means of ablationlaser radiation cannot be used for such methods. Instead, control dataare required to operate the laser for isolating the volume to be removedfrom the cornea. One such procedure for eye surgery is described in U.S.Pat. Nos. 6110166 and 7131968. Different volume forms are shown in US6110166 and it is mentioned that the proper volume can be chosen by aperson skilled in the art.

DE 102006053118 A1 describes the production of control data for thevolume-isolating correction of defective vision.

It is known from DE 102006053120 A1 and DE 102006053119 A1 from CarlZeiss Meditec AG to base the production of such defective vision on datawhich give the optical refraction power of spectacles suitable forcorrecting defective vision. It is also known from this publisheddocument, which thus describes a method of the mentioned type and adevice of the mentioned type, to use data which also bring about acorrection of an astigmatism or corrections of higher-order aberrations.By using data for defective vision which are intended for a conventionalspectacle correction, the approach known from DE 102006053120 A1achieves a considerable simplification in pre-operative eye measurement,as the production of spectacle correction data is daily practice inophthalmology. However, this simplification also means a degree oflimitation of the possible correction results, because inevitably onlycorrections which would also be possible with normal spectacles can beachieved. It is also to be taken into account here that corrections suchas are possible e.g. with varifocals are ruled out for the approachaccording to DE 102006053120 A1 as such corrections always assume that,depending on the viewing direction, the axis of vision passes throughthe spectacle lens at different points, which makes it possible to beable to bring different optical properties of the spectacles to bear fordifferent viewing directions (e.g. reading directed more downwards, orviewing directed more into the distance). This does not apply in thecase of refractive surgery on the cornea because movement of the eyeobviously causes the cornea to move as well when the direction ofviewing changes. Thus, unlike with a spectacle lens, there is no changein the point where the optical axis penetrates the cornea when theeyeball rotates. The approach known from DE 102006053120 A1 can thusconsequently use only comparatively simple spectacle defective-visioncorrection data as an input variable for control data, with theconsequence of correspondingly limited possibilities of correction.

The precision with which the necessary cut surfaces are produced is ofgreat importance for volume-isolating correction of defective vision.Unlike with a laser keratome, the position of the cut surfaces has adirect effect on the quality of the optical correction. With theconventional LASIK method, on the other hand, the precision with whichthe laser ablation is carried out is the only important factordetermining the quality of the optical correction. This can already beseen from the fact that the cornea lamella is or has been produced in alarge number of operations with a relatively crudely operatingmechanical knife.

As the exact positioning of the eye is important for the precisionproduction of the cut surfaces, the state of the art, for example WO2005/011547 A1, proposes that a contact glass, against which the corneais pressed, can be used in laser-surgery devices. This contact glassserves to fix the eye.

However, the precise position of the eye is not the only importantfactor for the precision of the cut surfaces; the shape of the corneamust also be known. As this varies from patient to patient withinspecific ranges, the contact glass also serves to give the cornea frontsurface a fixed, defined shape. When pressing the front of the corneaagainst the contact glass, there is consequently a deformation of thecornea which varies in size, depending on the deviation of the curvatureof the contact glass from the natural curvature of the cornea of therespective patient.

If the position of the cut surfaces is important for the opticalcorrection, i.e. if not just a lamella is isolated and the volume to beremoved is removed by ablation, the deformation of the cornea isessential when determining the target coordinates for producing the cutsurfaces. Therefore it is known in the state of the art to take intoaccount the deformation by subjecting the previously determined targetpoints to a coordinate transformation. In the named WO publication, thistransformation is called a “contact pressure transformation” and thereare transformation equations for a combination of spherical contactglass and spherical cornea front surface. DE 102008017293 A1 from CarlZeiss Meditec AG complements these transformation equations with theresult that coordinate transformation can also be carried out ondifferent types of contact glasses and cornea curvatures.

The invention thus relates to the concept of carrying out a correctionof the optical imaging errors of the human eye by cutting, by means oflaser radiation within the cornea, a volume of tissue which is thenremoved from the cornea. A selective change of the optical refractionpower of the cornea is thereby achieved. This change is localized, i.e.in the area of the cornea from which the tissue volume is removed. Thepupil of the eye is usually taken as a basis.

The removal of the cut volume changes the geometry, i.e. the curvatureof the cornea surface. In order that a desired correction of defectivevision is achieved, the cut volume to be removed must therefore havespecial properties with regard to its shape.

The cut volume is usually circumscribed by three boundary surfaces,based on classic LASIK methods. An anterior boundary surface is formedat a constant distance under the cornea. This is particularly simple ifthe cornea is flattened by a flat contact glass. As this cut surfacedirectionally lies furthest forward it is called anterior surface or, onthe basis of the known LASIK methods, flap surface.

Furthermore, the volume is limited by a deeper-lying cut surface whichis called posterior cut surface or, because the volume can be seen as alenticle, as lenticle surface. Therefore, it is ensured that overall thevolume to be removed changes the curvature of the cornea front surface.One of the two surfaces, usually the posterior one, generally has ageometry which is decisive for correcting defective vision.

In principle, it could be conceived to design the anterior and posteriorsurfaces such that they have a common cutting line. Firstly, this is notpossible when correcting long-sightedness as there the volume to beremoved must be thinner in the centre, i.e. in the area of the axis ofvision, than at the edge. Secondly, when correcting farsightedness itmight also be wished, for operational reasons, to ensure a certainminimum thickness of the volume at the edge in order to be able toremove it easily. The anterior surface and the posterior surface aretherefore connected via a so-called lenticle edge surface.

SUMMARY

The cut volume is made removable by these three cut surfaces, as thevolume is then completely or almost completely enclosed by the cutsurfaces. The absolute position and relative extent of the surfaces inthe cornea fix the zone within which the optical effect occurs afterremoval of the cut volume between these surfaces. Here, as alreadymentioned, the pupil of the eye is usually taken as basis. This approachleads to both cut surfaces, namely the anterior and posterior cutsurface, of which one or both can be optically effective, having to beconnected to a closed volume which must have a suitable position withinthe cornea.

The object of the first variant of the invention is to develop a deviceof the mentioned type or a method of the mentioned type to the effectthat control data can be produced for the surgical correction ofdefective vision with as little computation as possible, andsimultaneously, more complex corrections can also be achieved.

This object is achieved according to the invention in the first variantwith a device of the type named at the outset in which the radius ofcurvature R_(CV)* varies locally and satisfies the following equation:

R _(CV)*(r,φ)=1/((1/R _(CV)(r,φ))B _(COR)(r,φ)/(n _(c)-1))+F,

wherein R_(CV)(r,φ) is the local radius of curvature of the corneabefore the volume is removed, n_(c) is the refractive index of thematerial of the cornea, F is a coefficient, and B_(COR)(r,φ) is thelocal change in optical refraction power required for the desiredcorrection of defective vision in a plane lying in the vertex of thecornea, wherein there are at least two radii, r1 and r2, for whichB_(COR)(r=r1,φ)≠B_(COR)(r=r2,φ) holds true.

This object is further achieved according to the invention in the firstvariant with a method for generating control data for a laser of thetype named at the outset, wherein the radius of curvature R_(CV)* varieslocally and satisfies the following equation:

R _(CV)*(r,φ)=1/((1/R _(CV)(r,φ))+B _(COR)(r,φ)/(n _(c)-1))+F,

wherein R_(CV)(r,φ) is the local radius of curvature of the corneabefore the volume is removed, n_(c) is the refractive index of thematerial of the cornea, F is a coefficient, and B_(COR)(r,φ) is thelocal change in optical refraction power required for the desiredcorrection of defective vision in a plane lying in the vertex of thecornea, wherein there are at least two radii, r1 and r2, for whichB_(COR)(r=r1,φ) B_(COR)(r=r2,φ) holds true.

In the first variant, the invention provides a control variable or areference variable on the basis of which the volume to be removed andthus the cut surface isolating this volume in the cornea can becalculated as precisely as possible. It defines an equation for theradius of curvature which the cornea is to have after the removal of thevolume isolated by the treatment device or the method. The volume to beremoved can be calculated in an analytically precise manner with thisequation.

Upon closer inspection the equation used according to the invention inthe first variant to calculate the volume to be removed differssubstantially from the approach such as was used in DE 102006053120 A1.A different function is used which no longer takes into account theoptical refraction power of spectacles which lie at a distance to theeye, but a distribution of optical refraction power which, written incircular coordinates, varies at least radially. Additionally, thisdistribution of optical refraction power with which the new radius ofcurvature which the cornea must have after the surgical correction iscalculated no longer lies at a distance from the cornea, but gives theneed for correction in a plane which lies in the vertex of the cornea.The invention adopts the analytical approach of DE 102006053120 A1 andsimultaneously abandons the spectacle-correction values used there,introducing a radially varying distribution of optical refraction powerwhich reproduces the need for correction of the plane lying in thevertex of the cornea.

Thus, without the calculation effort being significantly increased, amuch more extensive correction of defective vision is possible. Forexample, a correction value which corresponds to the previousspectacle-correction value can now be applied in a central area aboutthe optical axis, e.g. in the radius of the phototopic pupil and otheroptical refraction power values can be used for greater diameters. Thusa presbyopia of the eye can be dealt with by carrying out in the centralarea, i.e. in the radius of the phototopic pupil, a correction of nearvision (comparable with reading spectacles) and a correction of distantvision (comparable with distance spectacles).

The volume is now determined or can now be determined according to theinvention via the equation such that the cornea displays the definedradius of curvature after removal of the volume. A particularly easilycalculable and above all also simply achievable (but by no means theonly) definition of the volume, limits the volume by a boundary surfacewhich comprises an anterior and a posterior surface part, wherein theanterior surface part lies at a constant distance d_(F) from the corneafront surface. The terms “anterior” and “posterior” correspond to theusual medical nomenclature. An additional edge surface is necessary(when correcting farsightedness) or advantageous in order to connect thetwo surface parts and simultaneously guarantee a minimum edge thickness.

Because the anterior surface part is at a constant distance from thecornea surface the formation of this surface part is particularlysimple. Naturally, the posterior surface part is then not necessarily ata constant distance from the cornea front surface. The opticalcorrection takes place by shaping the posterior surface part.Calculation effort is considerably simplified by this approach, as aspherical surface part (the anterior surface part) is particularlysimple to calculate and the calculation effort is concentrated on thedetermination of the posterior surface part. With such an approach, theposterior surface part has a curvature pattern which can be identical,apart from an additive constant, to that of the cornea front surfaceafter removal of the volume. The distance between the anterior surfacepart and the cornea front surface is reflected in the constant.

The radial dependency, present according to the invention in the firstvariant, of the distribution of optical refraction power means that,viewed in polar coordinates, there are at least two radii for all anglesin which there are different values for the distribution of opticalrefraction power.

The distribution of optical refraction power used may be present as aresult of a calculation using wave-front measurement or topographymeasurement of the cornea front of the cornea. Accordingly, the equationaccording to the invention on which the calculation of the volume of thecornea is based also provides a local radius of curvature of the cornea.The coordinates system chosen is preferably referenced to the vertex ofthe cornea.

If the topography Z_(CV):R²→R³ (quantity of all points Z_(CV)(r,φ) whichlie on the front of the cornea) is known the local radius of curvatureR_(CV)(z(r,φ)) can be determined for example by a best matching of asphere surface with the radius R to the surface Z_(CV) in aninfinitesimal radius about the point z_(CV)(r,φ). The fitting of acurvature circle in radial direction alone can also be used. Then:

${R_{CV}\left( {r,\phi} \right)} = \frac{\sqrt{1 + \left( {\frac{\partial}{\partial r}{z_{CV}\left( {r,\phi} \right)}} \right)^{2}}}{{\frac{\partial^{2}}{\partial r^{2}}{z_{CV}\left( {r,\phi} \right)}}}$

In this way the desired distribution of the radius of curvature of thefront of the cornea R_(CV)*(r,φ), which is to be achieved by therefraction correction B_(COR)(r,φ) is obtained by means of the equationaccording to the invention.

The site-specific refraction correction B_(COR)(r,φ) can also berepresented in the form of a wave-front. These wave-fronts are oftendescribed in practice by Zernike polynomials. In other words, themathematical description of the refraction correction by locallymodifiable optical refraction power forces can be converted directlyinto a set of Zernike coefficients. Suitable methods for this are knownto a person skilled in the art. As an example, reference may be madehere to the determination of the spectacle equivalents of thesphere/cylinder/axis from the Zernike coefficient Z_(2,i) and sphericalaberration (represented by Z_(4.0)). This conversion can be extendedanalogously to further Zernike orders, which then leads to a general,locally modifiable optical refraction power, also known to specialistsas higher-order errors (e.g. coma).

The thickness profile Δz(r,φ) of the volume to be removed is determinedor can be determined according to the invention by the topographyz_(CV)*(r,φ) of the cornea after the removal of the volume having thelocal radius of curvature R_(CV)*(r,φ) then:

z _(CV)*(r,φ)=z _(CV)(r,φ)−Δz(r,φ).

If an isolated volume is removed from the cornea Δz(r,φ) is alwayspositive. However, this is not a binding condition for the correction.It is likewise possible to change the refractive correction and,associated with this, the radius of the cornea front side by introducingan additional volume into the cornea. In this case Δz(r,φ) is alwaysnegative. Mixed cases are also possible in which Δz(r,φ) has bothpositive and negative areas. In practice this is the case if for examplea small refractive correction for distant vision in cases of myopia isto be effected by extraction of tissue and simultaneously a correctionof presbyopia by implantation of a small lens in the central area of theoptical zone. In this case the thickness of the implant may definitelybe greater than the thickness of the volume of tissue to be removed forcorrecting myopia and thus Δz(r,φ) have positive values in the centralarea and negative values in the edge area.

The thickness profile Δz(r,φ) of the volume results from the differencein topographies. If the desired topography after the correctionz_(CV)*(r,φ) is known the thickness profile is also determined.

A person skilled in the art can now use analysis or suitable arithmeticmethods to determine z_(CV)*(r,φ) from R_(CV)*(r,φ) by doubleintegration over the surface. The two integration constants occurringare chosen such that for example the desired treatment diameter forrefractive correction forms and simultaneously the volume to be removedis minimized.

In particular it is preferred in the first variant that, whendetermining the control data, the device fixes the local change inoptical refraction power B_(COR)(r,φ) such that there is acharacteristic radius r_(ch) for which the radial function of the changein optical refraction power B_(COR)(r,φ) is piecewise constant, forwhich thusB_(COR)(r<r_(ch),φ=const)=B_(a)≠B_(b)=B_(COR)(r>r_(ch),φ=const).

The distribution of optical refraction power used for correction can, asalready mentioned, have different values in specific areas of the pupil,e.g. a central area as well as an edge area, in order to achieve anoptical correction which achieves optimum results even with greatlyvarying sight conditions or is individually best adapted, e.g. in thecase of farsightedness in old age (presbyopia).

In particular it is preferred that, when determining the control data,the device fixes the local change in optical refraction powerB_(COR)(r,φ) such that there is a characteristic radius r_(ch) for whichthe radial function of the change in optical refraction powerB_(COR)(r,φ) is piecewise constant, for which thusB_(COR)(r<r_(ch),φ=const)=B_(a)≠B_(b)=B_(COR)(r>r_(ch),φ=const).

There can be a continuous transition between the partly constant valuesof the changes in optical refraction power. For this version it istherefore expedient that, when determining the control data, the devicefixes the local change in optical refraction power B_(COR)(r,φ) suchthat there are two radii r_(a) and r_(b) for which the radial functionof change in optical refraction power B_(COR)(r,φ) is piecewiseconstant, for which thusB_(COR)(r<r_(a),φ=const)=B_(a)≠B_(b)=B_(COR)(r>r_(b),φ=const), whereinthe radial function of the change in optical refraction powerB_(COR)(r,φ) passes continuously from B_(a) to B_(b) in the transitionarea between r_(a) and r_(b).

The local change in optical refraction power B_(COR)(r,φ) can, asspecial case, have symmetries which make it possible to separate therelationships between coordinates. This makes possible for example thefollowing notations during production of control values:

-   -   B_(COR)(r,φ)=B₁ (r) B₂(φ) (multiplicative separation approach)    -   B_(COR)(r,φ)=B₁ (r)+B₂(φ) (additive separation approach).

A special case of the separation results if the optical refraction powerdistribution is not angle-dependent. As this is particularly simple interms of calculation it is preferred that, when determining the controldata, the local change in optical refraction power is or will be fixedin an angle-independent manner.

It should be pointed out quite basically that optical refraction powerand radius of curvature can be transformed into each other by a simpleequation. Thus: B=(n_(c)-1)/R, wherein B is the optical refraction powerand R the radius allocated to this optical refraction power. Thus,within the framework of the invention, it is possible at any time toalternate between radius approach and optical refraction power approachor representation. The equation to be used when determining control datain optical refraction power representations is:

${B_{CV}^{*}\left( {r,\phi} \right)} = \frac{1}{\frac{1}{{B_{CV}\left( {r,\phi} \right)} + {B_{COR}\left( {r,\phi} \right)}} + \frac{F}{\left( {n_{C} - 1} \right)}}$

When the radius of the cornea surface is mentioned here, the opticalrefraction power can also be used completely analogously, with theresult that all statements made here in connection with the radius ofthe cornea surface self-evidently also apply analogously to therepresentation or consideration of the optical refraction power if R isreplaced by B according to the named connection.

In the second variant, the object of the invention is to provide, forcorrection of defective vision by laser surgery in which correctionsurfaces essential for the correction result are formed as a cut surfacein the eye, a method as well as a device for calculating control datawith which any correction surfaces can be used and sufficient account isstill taken of the influences of a contact glass.

This object is achieved according to a second version of the inventionby a method for generating control data which are adapted to control alaser for the surgical correction of the defective vision of an eye of apatient, wherein, during operation of the laser the cornea is deformedby pressing its anterior side against a contact surface, wherein, in themethod, a correction surface is predetermined for the non-deformedcornea, which correction surface is to be generated for correction ofdefective vision as a cut surface in the cornea, and wherein, in themethod, during operation of the laser, the deformation of the corneaduring operation of the laser is taken into account by a transformationof the coordinates of points in the non-deformed cornea into coordinatesof the same points in the deformed cornea, wherein

a) several points lying in the correction surface or in an approximationsurface derived therefrom are selected and its coordinates transformedby means of the transformation in order to obtain transformed points,

b) an interpolation surface is adapted to the transformed points byinterpolation and

c) target points lying on the interpolation surface (I′) are selectedand used for generating control data.

This object is further achieved according to the second version of theinvention by a device for generating control data which are adapted tocontrol a laser for the surgical correction of the defective vision ofan eye of a patient, wherein, during operation of the laser, the corneais deformed by pressing its anterior surface against a contact surfaceand wherein a correction surface is predetermined for the non-deformedcornea, which correction surface is to be generated for correction ofdefective vision as a cut surface in the cornea, and wherein the device,when generating the control data, takes into account the deformation ofthe cornea during operation of the laser by a transformation of thecoordinates for points in the non-deformed cornea into coordinates ofthe same points in the deformed cornea, wherein

a) the device, when generating the control data, selects several pointslying in the correction surface or in an approximation surface derivedtherefrom and transforms its coordinates by means of the transformationin order to obtain transformed points,

b) the device, when generating the control data, adapts an interpolationsurface to the transformed points by interpolation and

c) the device, when generating the control data, selects target pointslying on the interpolation surface and uses them to generate the controldata.

In the second variant, the invention starts from the situation that thecornea is deformed if the cornea front surface is given a specific shapein that the contact glass mentioned at the outset is pressed against it.Furthermore, the second variant of the invention assumes that thedeformation of the cornea can be reproduced by a coordinatetransformation which converts the coordinates of points in thenon-deformed cornea into transformed coordinates of the same points inthe deformed cornea.

Building on these known transformations, the invention provides for anyshape of correction surfaces which are to be produced as cut surfaces inthe cornea to be treated suitably in order to take into account theeffect of cornea deformation. The process according to the secondvariant of the invention allows any correction surfaces to be treated.In particular, there is no longer a limitation to spherical surfacessuch as were previously discussed in the state of the art. As a result,the cornea deformation can also be taken into account for any,particularly non-rotation-symmetrical, cut surfaces. While sphericalcorrection surfaces or correction surfaces which represent a combinationof a sphere and a cylinder part (such as are known when correctingastigmatism) can be treated analytically in respect of the coordinatetransformation and essentially only the vertex and an edge point for asphere or two edge points for a combination of sphere and cylinder needbe considered in the transformation, such an approach is not possiblewith correction surfaces which effect higher-order corrections or arealso non-rotation-symmetrical. Such correction surfaces can also betreated with the principle according to the invention in respect ofcornea deformation.

This process allows any shape of correction surface to be used and stilltake into account the effect of deformation on the cornea for thesecorrection surfaces. It is also no longer essential to adapt thecurvature of the contact glass as precisely as possible to the curvatureof the natural cornea in order to minimize errors caused by deformationsif the correction surface is to have a shape other than the customaryspherical or spherical cylindrical shapes.

Furthermore, the interpolation surface I′ obtained by interpolation (oroptionally approximation) makes it possible to fix path curves whichallow rapid treatment. If, on the other hand, it were wished totransform the target points themselves or a path curve which connectsthe target points, it would not automatically be ensured that thetransformed target points or the transformed path curve wouldautomatically still be optimal with respect to treatment speed. On thebasis of the virtually arbitrary distortions which can be caused by thecontact pressure transformation, it would be better to assume that theoptimum is no longer reached.

Depending on the definition of the correction surface, a really largenumber of characteristic points may be necessary to be able to carry outthe interpolation after the transformation of the characteristic pointswith sufficient accuracy. In such cases, a further embodiment of theinvention may be advantageous which firstly derives an approximationsurface from the correction surface. A smoothing process or also anapproximation process can be used. The smoothing can in particular be adeep-pass filtering. An approximation by an analytically more easilydescribed approximation surface is also possible. A particular advantageis achieved if an approximation surface is chosen which has a 2-, 3- or4-fold angle symmetry. The approximation surface, not the correctionsurface itself, is then subjected to the transformation. In order totake into account the differences between the approximation surface andthe correction surface, a deviation between the correction surface andthe approximation surface is also determined. This deviation isexpediently determined at the characteristic points selected for thetransformation. However, it is also possible to determine a generaldeviation function or a deviation matrix. This deviation, which is notsubjected to the transformation, is then used to correct theinterpolation surface. This approach thus assumes that the deviation inrespect of the transformation is essentially invariant. Thecomputational effort can be considerably reduced in this embodiment.

The points to be selected for the transformation preferably take accountof symmetries of the correction surface. Furthermore, it is expedient totake into account invariances of the contact pressure transformationwhen choosing the points to be transformed which can also be regarded ascharacteristic points.

The features described here can naturally be combined as desired withone another, providing they do not contradict each other technically. Inparticular features of the first variant of the invention can becombined with features of the second variant of the invention.

The methods according to the invention of all variants for generatingthe control data can be carried out without recourse to humaninvolvement. In particular they can be carried out by a computer whichcarries out the method according to the invention under the control of aprogram according to the invention and determines the control data forthe laser from the corresponding presets. In particular when generatingcontrol data there is no need for the participation of a doctor as thereis no therapeutic procedure involved in generating the control data. Atherapeutic procedure takes place only when the previously determinedcontrol data are employed.

Where a method or individual steps of a method for generating controldata for surgical correction of defective vision are described in thisdescription, the method or individual steps of the method can be carriedout using a correspondingly adapted device. This applies analogously tothe explanation of the mode of operation of a device which carries outthe method steps. To this extent the device and method features of thisdescription are equivalent. In particular it is possible to realize themethod with a computer on which a corresponding program according to theinvention is executed.

The above summary is not intended to describe each illustratedembodiment or every implementation of the subject matter hereof. Thefigures and the detailed description that follow more particularlyexemplify various embodiments.

BRIEF DESCRIPTION OF THE DRAWINGS

Subject matter hereof may be more completely understood in considerationof the following detailed description of various embodiments inconnection with the accompanying figures, in which:

FIG. 1 is a schematic representation of a treatment device or of atreatment apparatus for correcting defective vision;

FIG. 2 is a schematic representation of the structure of the treatmentapparatus of FIG. 1;

FIG. 3 is a presentation showing the principle of introducing pulsedlaser radiation into the eye when correcting defective vision with thetreatment apparatus of FIG. 1;

FIG. 4 is a further schematic representation of the treatment apparatusof FIG. 1;

FIG. 5 is a schematic sectional representation through the corneashowing a volume to be removed for correcting defective vision;

FIG. 6 is a section through the cornea after removal of the volume ofFIG. 5;

FIG. 7 is a sectional representation similar to that of FIG. 5;

FIG. 8 is a schematic sectional representation through the cornea toillustrate the volume removal;

FIG. 9 is a diagram with possible patterns of a distribution of opticalrefraction power which is used when determining the volume to beremoved;

FIG. 10 is a flowchart for determining the volume to me removed;

FIG. 11 is a graph illustrating the geometrical transformation methodfor a specific angle about the z axis; and

FIG. 12 is a graph illustrating a transformation method simplifiedvis-à-vis FIG. 11.

While various embodiments are amenable to various modifications andalternative forms, specifics thereof have been shown by way of examplein the drawings and will be described in detail. It should beunderstood, however, that the intention is not to limit the claimedinventions to the particular embodiments described. On the contrary, theintention is to cover all modifications, equivalents, and alternativesfalling within the spirit and scope of the subject matter as defined bythe claims.

DETAILED DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a treatment apparatus 1 for an eye-surgery procedure whichis similar to that described in EP 1159986 A1 or in U.S. Pat. No.5,549,632. By means of a treatment laser radiation 2 the treatmentapparatus 1 effects a correction of defective vision on an eye 3 of apatient 4. Defective vision can include hyperopia, myopia, presbyopia,astigmatism, mixed astigmatism (astigmatism in which there is hyperopiain one direction and myopia in a direction lying at right anglesthereto), aspherical errors and higher-order aberrations. In theembodiment described, the treatment laser radiation 2 is applied as apulsed laser beam focused into the eye 3. The pulse duration in thiscase is e.g. in the femtosecond range, and the laser radiation 2 acts bymeans of non-linear optical effects in the cornea. The laser beam hasshort laser pulses of e.g. 50 to 800 fs (preferably 100-400 fs) with apulse repetition frequency of between 10 and 500 kHz. In the embodimentdescribed, the modules of the apparatus 1 are controlled by anintegrated control unit, which, however, can of course also be formed asa stand-alone unit.

Before the treatment apparatus is used, the defective vision of the eye3 is measured with one or more measuring devices.

FIG. 2 shows the treatment apparatus 1 schematically. In this variant ithas at least two devices or modules. A laser L emits the laser beam 2onto the eye 3. The operation of the laser L in this case is fullyautomatic, i.e. in response to a corresponding start signal the laser Lstarts to deflect the laser beam 2 and thereby produces cut surfaceswhich, in a manner to be described, are built up and isolate a volume inthe cornea. The laser L receives the control data necessary foroperation beforehand from a planning device P as a control data set, viacontrol lines that are not described in more detail. The data aretransmitted prior to operation of the laser L. Naturally, communicationcan also take place wirelessly. As an alternative to directcommunication, it is also possible to arrange the planning unit Pphysically separated from the laser L, and to provide a correspondingdata transmission channel.

Preferably, the control data set is transmitted to the treatmentapparatus 1 and more preferably, the operation of the laser L is blockeduntil there is a valid control data set at the laser L. A valid controldata set can be a control data set which in principle is suitable foruse with the laser L of the treatment device 1. Additionally, however,the validity can also be linked to the passing of further tests, forexample whether details, additionally stored in the control data set,concerning the treatment apparatus 1, e.g. an appliance serial number,or concerning the patient, e.g. a patient identification number,correspond to other details that for example have been read out or inputseparately at the treatment device as soon as the patient is in thecorrect position for the operation of the laser L.

The planning unit P produces the control data set that is made availableto the laser unit L for carrying out the operation from measurement dataand defective-vision data which have been determined for the eye to betreated. They are supplied to the planning unit P via an interface Sand, in the embodiment example represented, come from a measuring deviceM which has previously taken measurements of the eye of the patient 4.Naturally, the measuring device M can transfer the correspondingmeasurement and defective-vision data to the planning device P in anydesired manner.

Transmission can be by means of memory chips (e.g. by USB or memorystick), magnetic storage (e.g. disks), by radio (e.g. WLAN, UMTS,Bluetooth) or wired connection (e.g. USB, Firewire, RS232, CAN-Bus,Ethernet etc.). The same naturally also applies with regard to the datatransmission between planning device P and laser L.

A direct radio or wired connection of measurement device M to treatmentdevice 1 with regard to data transfer which can be used in a variant hasthe advantage that the use of incorrect measurement and defective-eyedata is excluded with the greatest possible certainty. This applies inparticular if the patient is transferred from measuring device M ormeasuring devices to the laser L by means of a storage device (notrepresented in the Figure) which interacts with measuring device M orlaser L such that the respective devices recognize whether the patient 4is in the respective position for measurement or introduction of thelaser radiation 2. By bringing the patient 4 from measuring device M tolaser L the transmission of measurement and error-correction data to thetreatment device 1 can also take place simultaneously.

Preferably it is ensured by suitable means that the planning device Palways produces the control data set belonging to the patient 4 and anerroneous use of a false control data set for a patient 4 is as good asexcluded.

The mode of operation of the laser beam 2 is indicated schematically inFIG. 3. The treatment laser beam 2 is focused into the cornea 5 of theeye 6 by means of a lens which is not shown in more detail. As a resultthere forms in the cornea 5 a focus that covers a spot 6 and in whichthe energy density of the laser radiation is so high that, incombination with the pulse length, a non-linear effect in the eyeresults. For example, each pulse of the pulsed laser radiation 2 canproduce at the respective spot 6 an optical break-through in the cornea5 which, in turn, initiates a plasma bubble, indicated schematically inFIG. 3. As a result, tissue in the cornea 5 is cut disrupted this laserpulse. When a plasma bubble forms, the tissue layer disruption covers alarger region than the spot 6 covered by the focus of the laserradiation 2, although the conditions for producing the break-through areachieved only in the focus. In order for an optical break-through to beproduced by every laser pulse, the energy density, i.e. the fluence, ofthe laser radiation must be above a certain threshold value which isdependent on pulse length. This relationship is known to a personskilled in the art from, for example, DE 69500997 T2.

Alternatively, a tissue-cutting effect can also be produced by thepulsed laser radiation by sending several laser radiation pulses into aregion, wherein the spots 6 overlap for several laser radiation pulses.Several laser radiation pulses then act together to achieve atissue-cutting effect.

The type of tissue cutting which the treatment apparatus 1 uses is,however, no further relevant for the description below, although pulsedtreatment laser radiation 2 is described in this description. Forexample a treatment apparatus 1 such as is described in WO 2004/032810A2 can be used. A large number of laser-pulse foci forms a cut surfacein the tissue, the form of which depends on the pattern with which thelaser-pulse foci are/become arranged in the tissue. The patternspecifies target points for the focus position at which one or morelaser pulse(s) is (are) emitted and defines the form and position of thecut surface.

In order now to carry out a correction of defective vision, material isremoved from a region within the cornea 5 by means of the pulsed laserradiation by cutting tissue layers thus isolating the material and thenmake it possible for material to be removed. The removal of materialeffects a change in the volume of the cornea which results in a changein the optical imaging effect of the cornea 5, which change iscalculated exactly such that the previously determined defective visionthus is/becomes corrected as much as possible. To isolate the volume tobe removed, the focus of the laser radiation 2 is directed towardstarget points in the cornea 5, generally in an area which is locatedbeneath the epithelium and the Bowman's membrane and above the Decemet'smembrane and the endothelium. For this purpose the treatment apparatus 1has a mechanism for shifting the position of the focus of the laserradiation 2 in the cornea 5. This is shown schematically in FIG. 3.

In FIG. 4, elements of the treatment apparatus 1 are shown only as longas they are necessary to understand the shifting of the focus. Asalready mentioned, the laser radiation 2 is bundled in a focus 7 in thecornea 5, and the position of the focus 7 in the cornea is shifted suchthat, to produce cut surfaces, energy from laser radiation pulses isintroduced into the tissue of the cornea 3 focused at various points.The laser radiation 2 is provided by a laser 8 as pulsed radiation. Anxy scanner 9 which, in one variant, is realized by two substantiallyorthogonally deflecting galvanometric mirrors, deflects the laser beamof the laser 8 in two dimensions such that there is a deflected laserbeam 10 after the xy scanner 9. The xy scanner 9 thus effects a shiftingof the focus 7 substantially perpendicular to the main direction ofincidence of the laser radiation 2 into the cornea 5. To adjust thedepth position a z scanner 11 which is realized, for example, as anadjustable telescope, is provided in addition to the xy scanner 9. The zscanner 11 ensures that the z position of the focus 7, i.e. its positionon the optical incidence axis, is changed. The z scanner 11 can bearranged before or after the xy scanner 9. The coordinates designated x,y, z in the following thus relate to the deflection of the position ofthe focus 7.

The allocation of the individual coordinates to the spatial directionsis not essential for the operating principle of the treatment apparatus1; but to simplify the description, in the following the coordinatealong the optical axis of incidence of the laser radiation 2 is alwaysdesignated z, and x and y designate two coordinates orthogonal to oneanother in a plane perpendicular to the direction of incidence of thelaser beam. It is naturally known to a person skilled in the art thatthe position of the focus 7 in the cornea 5 can also be describedthree-dimensionally by other coordinate systems, in particular that thecoordinate system need not be a rectangular system of coordinates. Thusit is not essential for the xy scanner 9 to deflect around axes that areat right angles to one another; rather, any scanner capable of shiftingthe focus 7 in a plane in which the incidence axis of the opticalradiation does not lie can be used. Oblique-angled coordinate systemsare thus also possible.

Further, non-Cartesian coordinate systems can also be used to describe,or control, the position of the focus 7, as will also be explainedfurther below. Examples of such coordinate systems are sphericalcoordinates as well as cylindrical coordinates.

To control the position of the focus 7, the xy scanner 9 as well as thez scanner 11, which together realize a specific example of athree-dimensional focus-shifting device, are controlled by a controlapparatus 12 via lines not described in more detail. The same applies tothe laser 8. The control apparatus 3 ensures a suitably synchronousoperation of the laser 8 as well as the three-dimensional focus-shiftingdevice, realized by way of example by the xy scanner 9 and the z scanner11, with the result that the position of the focus 7 is shifted in thecornea 5 such that, ultimately, a specific volume of material isisolated, wherein the subsequent volume removal effects a desiredcorrection of defective vision.

The control apparatus 12 operates according to predetermined controldata which predetermine the target points for shifting the focus. Thecontrol data are generally collected in a control data set. In oneembodiment, this predetermines the coordinates of the target points as apattern, wherein the sequence of the target points in the control dataset fixes the serial arrangement of the focus positions alongside oneanother and thus, ultimately, a path curve (also referred to hereinshort as a path). In one embodiment, the control data set contains thetarget points as specific reference values for the focus-shiftingmechanism, e.g. for the xy scanner 9 and the z scanner 11. To preparethe eye-surgery procedure, thus before the actual operation can becarried out, the target points and preferably also their order aredetermined in the pattern. There must be pre-planning of the surgicalprocedure to determine the control data for the treatment apparatus 1,the application of which then achieves an optimal correction ofdefective vision for the patient 4.

Firstly, the volume to be isolated in the cornea 5 and later removedmust be defined. As already described with reference to FIG. 2 thisrequires to establish the need for correction.

With regard to the nomenclature used in this description it may be notedthat the addition of an asterisk to values indicates that these arevalues which are obtained after a correction. On the justifiedassumption that a change in thickness of the cornea 5 substantiallymodifies the radius of curvature of the front face 15 of the corneafacing the air, but not the radius of curvature of the rear 16 of thecornea adjacent to the inside of the eye, the radius of curvature R_(CV)of the front of the cornea 15 is modified by the volume removal. Becauseof the modified curvature of the front having changed cornea surface15*, the cornea 5 reduced by the volume has a correspondingly modifiedimaging effect, with the result that there is now a corrected focus onthe retina 14.

To determine the pattern of the target points, the curvature to beachieved R_(CV)* of the cornea front surface 15* is thereforedetermined.

Using the value B_(COR), the curvature of the modified cornea frontsurface 15* is now set as follows:

R _(CV)*(r,φ)=1/((1/R _(CV)(r,φ))+B _(COR)(r,φ)/(n_(c)-1))+F,   (1)

In equation (1) n_(c) denotes the optical refraction power of thematerial of the cornea. The proper value is usually 1.376; B_(COR)denotes a change in optical refraction power which is necessary tocorrect defective vision. B_(COR) is radially dependent. By radialdependence is meant that there are two values r1 and r2 for the radius rfor which the change in optical refraction power has different values atall angles φ.

Examples of possible patterns of changes in optical refraction power areshown by way of example in FIG. 9 which shows the function B_(COR) indifferent exemplary curves Ka to Ke as a function of the radius r.

Ka is the conventional refractive index of spectacles from the state ofthe art according to DE 102006053120 A1, but already referenced to theplane of the vertex of the cornea in the representation of FIG. 9. Inthe cited state of the art there is no reason for such referencerelationship. It has been included here only for the purpose of bettercomparability with the exemplary curves Kb to Ke according to theinvention. The curve Kb is constant up to a radius which lies beyond aradius r_(s), and then falls. The radius r_(s) is thus the scotopicpupil radius, i.e. the pupil radius at night vision. The change inoptical refraction power according to curve Kc is partly constant as faras radius r_(s), wherein below a radius r_(p), which corresponds to thephotopic pupil radius, there is a sudden drop from a higher value to alower value. Such a variation of the correction in optical refractionpower over the cross-section of the pupil is particularly advantageousin the case of farsightedness in old age. Near vision usually occursunder good lighting, e.g. when reading. The pupil is then generallycontracted to the photopic pupil radius because of the good lighting.The correction in optical refraction power then necessary sets anoptimum adaptation to near vision, e.g. an optimum viewing distance ofapproximately 25 to 70 cm. For the other extreme case, namely nightvision, which is usually linked with looking into the distance (e.g.when driving at night), on the other hand, the pupil is opened to itsmaximum. Then, areas of the pupil which have a different (e.g. lower)value for correcting optical refraction power also contribute to opticalimaging. The human brain is capable of correcting imaging having suchvisual errors (different position of focus for the centre of the pupiland edge areas of the pupil) in visual perception. The correction ofoptical refraction power curves shown in the curves Kc or Kd thus allow,consciously accepting an imaging error, the enlargement of the focusdepth range, as the imaging error is compensated for by the brain.

The correction of optical refraction power then drops again from pupilradius r_(s). The unstepped drop in the correction of optical refractionpower to zero is advantageous from an anatomical point of view. Itallows, at the edge of the corrected range, i.e. at the edge of thevolume to be removed, an adaptation of the corrected cornea front radiuswhich is set, on the basis of the correction, to the original radius ofcurvature of the cornea, i.e. the pre-operative radius. Reverting to therepresentation of FIG. 5 this means that there is an adjustment of theseradii in the edge area of the volume to be removed at which the radiiR_(F) and R_(L) converge in the representation of FIG. 5. As a result,the transition from the new cornea front-side radius R*_(CV) whichoccurs in the area in which the volume 18 has been removed to theoriginal radius of curvature of the cornea R_(CV) is comparably soft.The optical correction is thus overall better, which can be achievedonly because of the radially varying the correction of opticalrefraction power.

The drop in the correction of optical refraction power to zero takesplace preferably in an area outside the darkened pupil radius, thus inan area of the cornea no longer relevant for vision.

The curve Kd shows a similar pattern, but here there is a smoothtransition from the first value of the change in optical refractionpower below r_(p) to the second value at r_(s). Also, by way of example,the first value here is lower than the second value. This can naturallyalso be used for the curve Kc, depending on the desired requirement forcorrection. Curve Ke shows a continuous decline.

The locally varying changes in optical refraction power, described withreference to FIG. 9, with radial dependence, are examples of a change inoptical refraction power which is used when determining the volume to beremoved in the operation.

The coefficient F expresses the optical effect of the change inthickness which the cornea experiences as a result of the surgicalprocedure and can be seen in a first approximation as a constantcoefficient which can be determined e.g. experimentally in advance. Fora highly accurate correction the coefficient can be calculated accordingto the following equation:

F=(1-1/n _(c))·Δz(r=0,φ)

Δz(r=0, φ) is the central thickness of the volume to be removed.

For a precise determination, R_(CV)* is iteratively calculated bydetermining in an nth calculation step the value Δz(r=0,φ) from thedifference 1/R_(CV)*(r=0,φ)-1/R_(CV) Δr=0,φ) and using the correspondingresult obtained from this for the change in thickness in the (n+1)thcalculation step as new value for R*_(CV). This can be carried out untilan abort criterion is met, for example if the difference in the resultfor the change in thickness in two successive iterations lies below asuitably fixed limit. This limit can for example be set as a constantdifference which corresponds to an accuracy of the refraction correctionthat is appropriate to the treatment.

In general the method represented in FIG. 10 can be carried out. In astep S1 the topography of the cornea is calculated from diagnosis data,as mentioned already at the start in the general section of thedescription. The radial curvature of the front 15 of the cornea isdetermined from this topography. This can also be directly determinedfrom the diagnosis data, instead of the topography data from step S1,with the result that step S2 is either placed after step S1 or diagnosisdata are directly evaluated as FIG. 10, shows by adding “(optional)”.Thus step S1 is optional.

Typical diagnosis data for step S2 are measurement data which describethe site-specific curvature of the cornea, for example the topographydata of cornea topographs (Scheimpflug, Placido projectors) or simplekeratometers which determine only the average curvature of the cornea onthe steepest and flattest meridian. It is likewise possible that theglobal curvature of the cornea is used as manual input parameter or thateven a fixed value is used if no specific adaptation appears necessary.

The local optical refraction power of the cornea is determined in a stepS3.

The required local change in optical refraction power B_(COR) isdetermined from data relating to the desired refractive correction in astep S4 and the local optical refraction power desired after thecorrection determined from this local change in optical refractionpower. The desired refractive correction can then be input directly aslocally varying optical refraction power or, as mentioned initially,equivalently also in the form of a general wave-front change which canthen be represented for example in the form of Zernike coefficients.

If the locally varying optical refraction power is used, there is thus aparticularly descriptive presentation if, instead of a local opticalrefraction power at a specific point, the average of the opticalrefraction power over a ring segment, in particular over a circularsurface, is displayed and entered.

It is likewise possible to incorporate diagnosis data concerning thepreoperative wave-front in order to derive the wave-front changes to berealized, which in turn leads to a specific target wave-front. Mixedforms in which the data of the subjectively determined refraction valuessphere/cylinder/axis are combined with the wave-front measurement dataare also possible.

The new local radius of curvature R*_(CV)(r,φ) is generated then in stepS5. Instead of the calculation of the local optical refraction powerB_(CV) in step S3, calculation can also take place directly with thelocal curvature R_(CV) from step S2 if the above equation (1) is used.It should be pointed out quite basically that optical refraction powerand radius of curvature can be transformed into each other by a simpleequation. Thus: B=(n_(c)-1)/R, wherein B is the optical refraction powerand R the radius allocated to this optical refraction power. Thus,within the framework of the invention, it is possible at any time toalternate between radius approach and optical refraction power approachor representation. The equation to be used when determining control datain optical refraction power representations is:

${B_{CV}^{*}\left( {r,\phi} \right)} = \frac{1}{\frac{1}{{B_{CV}\left( {r,\phi} \right)} + {B_{COR}\left( {r,\phi} \right)}} + \frac{F}{\left( {n_{C} - 1} \right)}}$

When the radius of the cornea surface is mentioned here, the opticalrefraction power can also be used completely analogously, with theresult that all statements made here in connection with the radius ofthe cornea surface self-evidently also apply analogously to therepresentation or consideration of the optical refraction power if R isreplaced by B according to the named dependency.

For the volume whose removal effects the above change in curvature ofthe cornea front surface 15 the boundary surface isolating the volume isnow defined in a step S6. Account is to be taken of what basic form thevolume is to have.

In a first variant by numerical methods known to a person skilled in theart a free from surface is defined which circumscribes the volume whoseremoval effects the change in curvature. The volume thickness requiredfor the desired modification in curvature is determined along the zaxis. This gives the volume a function of r,φ (in cylinder coordinates)and the boundary surface is defined based on the volume.

On the other hand an analytical calculation is delivered by thefollowing variant, already discussed in DE 102006053120 A1, in which theboundary surface of the volume is essentially built up from two surfaceparts, an anterior surface part facing the cornea surface 15 and anopposite posterior surface part. FIG. 5 shows the correspondingrelationships. The volume 18 is limited towards the cornea front 15 byan anterior cut surface 19 which is at a constant distance d_(F) belowthe cornea front surface 15. This anterior cut surface 19 is also calledflap surface 19 by analogy with the laser keratomes as it serves, incombination with an opening section towards the edge, to be able toraise a flap-shaped lamella from the cornea 5 from the cornea 5 beneath.This way of removing the previously isolated volume 18 is naturallypossible here also.

The anterior cut surface 19 is preferably spherical as then a radius ofcurvature which is smaller by the thickness of a lamella d_(F) than theradius of curvature R_(CV) can be defined.

To the rear the volume 18 which is to be removed from the cornea 5 islimited by a posterior cut surface 20 which already basically cannot beat a constant distance from the cornea front surface 15. The posteriorcut surface 20 is therefore formed such that the volume 18 has the formof a lenticle, which is why the posterior cut surface 20 is also calledlenticle surface. This surface is shown in FIG. 5 by way of example as alikewise spherical surface with a radius of curvature R_(L), wherein inFIG. 5 naturally the center of this curvature does not coincide with thecenter of curvature of the likewise spherical cornea front surface 15.The two surfaces 19, 20 are preferably connected at their edge by alenticle edge surface in order to completely circumscribe the volume tobe removed and simultaneously guarantee a minimum thickness at the edge.

FIG. 6 shows the situation after the volume 18 has been removed. Theradius of the modified cornea front surface 15* is now R_(CV)* and canfor example be calculated according to the previously describedequations. The thickness d_(L)=Δz(r=0,φ) of the removed volume 18governs the change in radius, as illustrated by FIG. 7. The lenticlesurface is simplified to be spherical in this figure. Consequently, theheight h_(F) of the ball cap defined by the flap surface 19, the heighth_(L) of the ball cap defined by the lenticle surface 20 and thethickness dL of the volume 18 to be removed are shown.

Due to the constant distance between cornea front surface 15 and flapsurface 19, the lenticle surface 20 defines the curvature of the corneafront surface 15* after the volume 18 has been removed.

If the coefficient F is to be taken into account during calculation, instep S7 the change in topography of the cornea are considered, too, i.e.the current central thickness is computed. Using the resulting value forthe coefficient F, steps S4 to S6 or S5 to S6 can then be carried outonce again or repeatedly in the form of an iteration.

The formation shown in the figures of the volume 18, as limited by aflap surface 19 at a constant distance from the cornea front surface 15and a lenticle surface 20, is only one variant for limiting the volume18. However, it has the advantage that the optical correction is givenessentially by only one surface (the lenticle surface 20), with theresult that the analytical description of the other surface part of theboundary surface is simple.

Furthermore, safety margins with regard to the distance between thevolume and cornea front surface 15 and cornea back surface 16 areoptimal. The residual thickness d_(F) between flap surface 19 and corneafront surface 15 can be set to a constant value, e.g. 50 to 200 μm. Inparticular it can be chosen such that the pain-sensitive epitheliumremains in the lamella which is formed by the flap surface 19 beneaththe cornea front surface 15. The formation of the spherical flap surface19 is also continuous with previous keratometer sections which isadvantageous in terms of acceptance of the method.

After producing the cut surfaces 19 and 20 the thus-isolated volume 18is then removed from the cornea 5. This is represented schematically inFIG. 9 which also shows that the cut surfaces 19 and 20 are produced bythe action of the incident treatment laser beam by exposure to a focussphere 21, for example by the arrangement of plasma bubbles alongsideone another, with the result that in a preferred embodiment the flapsurface 19 and the lenticle surface 20 are produced by suitablethree-dimensional shifting of the focus position of the pulsed laserradiation 2.

Alternatively in a simplified embodiment, however, merely the flapsurface 19 can also be formed, by means of pulsed laser radiation, bytarget points which define the curved cut surface 19 at a constantdistance from the cornea front surface 15, and the volume 18 is removedby laser ablation, for example by using an excimer laser beam. For this,the lenticle surface 20 can be defined as boundary surface of the arearemoved, although this is not essential. The treatment apparatus 1 thenoperates like a known laser keratome, but the cut surface 19 is producedusing curved cornea. The previously or subsequently described featuresare also possible in such variants, in particular as regards thedetermination of the boundary surface, its geometric definition anddetermining control parameters.

If both the lenticle surface 20 and the flap surface 19 are produced bymeans of pulsed laser radiation it is expedient to form the lenticlesurface 20 prior to the flap surface 19, as the optical result is betterwith the lenticle surface 20 (if not achievably only then) if there hasstill been no change in the cornea 5 above the lenticle surface 20.

As already explained in the general section of the description, both theexact positioning of the cornea and also precise knowledge of thecurvature of the cornea are essential for the correction of defectivevision described here. Only with knowledge of this curvature can forexample the described flap section be produced and the desiredcorrection surface as a cut surface in the form of the lenticle surfacebe achieved.

Therefore a contact glass is used which has a curved contact surface.The cornea is pressed against this. This process leads, as alreadydescribed initially, to a deformation of the cornea.

If a correction surface has been determined which is to be produced inthe eye as a cut surface, this correction surface naturally relates tothe non-deformed cornea. However, the cut surface is produced in thedeformed cornea, with the result that the correction surface or the cutsurface must be modified accordingly before finalizing the control data.This modification considers a predistortion of the correction surface orof the cut surface to be produced, wherein the surface is changed suchthat, after removing the contact glass, i.e. after the relaxation of thedeformation, the desired surface shape is still achieved.

This predistortion of the predetermined correction surface is carriedout by subjecting the predetermined correction surface to a coordinatetransformation which reproduces the deformation of the cornea. Suchcoordinate transformations are known from US 2007/0293851 A1, which isincorporated in full in this respect into this disclosure, and also fromDE 102008017293 A1, the disclosure of which is likewise incorporated infull.

As explained above, the locally modifiable refractive correctionB_(COR)(r,φ) is achieved by disrupting tissue layers in the cornea bymeans of pulsed laser radiation along cut surfaces F:=z(r,φ): R²→R³,with the result that a volume is enclosed which is then removed. Theshape of the front surface of the cornea is selectively changed as aresult of this step such that the desired correction is obtained. Forthis, for example, a treatment beam is focussed into the cornea of theeye 6.

The shape F_(A):=z_(A)(r, φ) of the anterior cut surface 19 and theshape F_(P):=z_(P)(r, φ) of the posterior cut surface 20 of the volume18 to be removed are essentially determined in that the thicknessprofile Δz(r, φ)=z_(A)(r, φ)−z_(P)(r, φ) of the circumscribed materialresults in the required change in shape of the cornea front surface 15after removal. Therefore, an exact, absolute positioning of theindividual laser shots in the micrometers range within the cornea 5 ofthe eye to be treated is essential in order to guarantee the accuraciesof the refractive correction, which is why the position of the cornea isfixed relative to the optical system of laser radiation, and the corneafront surface 15 is changed into a known shape by pressing the contactglass against the cornea 5 of the eye and e.g. mechanically fixing itthere by means of suction (cf. US 2008/234707 A1).

The contact glass changes the shape of the cornea front surface. Thedeformation is described in US 2007/0293851 with reference to FIGS.11-13 and is called contact pressure transformation (AT:R³→R³). As alsoin the incorporated published documents, variables which relate to thetransformed coordinate system are characterized in this description by asuperscript.

A correction surface which is also to be produced as a cut surface inthe eye is determined for the correction of defective vision. Optionallythere can also be more than one surface. By correction surface is meanthere any cut surface which must be produced in the eye and which iseffective for altering refraction in the eye. For example, the flapsurface is not included and the above-described embodiment whichconcentrates the optical correction in a single surface, namely thelenticle surface, is preferred. The correction surface can be determinedin any manner, for example using the principles named above. The3-dimensional cut surfaces are generated e.g. by arranging individuallaser beams alongside one another along a path curve to form cut linesand by arranging cut lines alongside one another to form cut surfaces.

This correction surface is now subjected to the coordinatetransformation, as will be explained below.

In the case of more elaborate corrections, in particular in the case ofcorrections which are not limited to a correction surface, which can beindicated by a sphere or optionally a sphere with a cylindrical portion,the correction surface can pose significant numeric problems if thecontrol data were produced first and then subjected to transformation.As in a system operating with pulsed laser radiation the extent of thephysical tissue disruption of an individual laser beam lies in the rangeof a few square micrometers and the whole cut surface is in the range ofapprox. 50 mm², the coordinates of approximately 10 million points wouldhave to be transformed.

In order to avoid this outlay on computation, only a subset, severaltimes smaller, of the points of the correction surface or cut surface,is selected as points f₁ of the surface F. The selection of the pointspreferably takes into account geometric properties of the cut surface Fwhich is to be produced in the non-deformed cornea. Preferably, anysymmetries of the cut surface as well as an invariance of the angleimaging in the contact pressure transformation (angle about the opticalaxis) are taken into account when choosing the points.

Once a subset of the possible points of cut surface F has been selectedin this way, these points are transformed with the contact pressuretransformation. An interpolation surface I′ is then adapted byinterpolation. This corresponds with sufficient precision to thetransformed correction surface F. The target points and the path(s)containing same which form part of the control data of the treatmentdevice are then fixed in the interpolation surface I′.

The method thus provides the following:

If the scanning device is later controlled such that every single focuspoint for producing the cut surface lies on the transformed cut surfaceF′:=z′(r,φ), the correct volume has been enclosed, as the removal of thecontact glass leads to a relaxation of the cornea which corresponds to aretransformation. Thus the following occurs:

1. Characteristic points f_(i) are selected on the correction surface Fand transformed into f_(i)′ T he points f_(i) are preferably chosen suchthat they represent geometric properties of the cut surface F in thenon-deformed cornea 5 (thus in the natural system). Advantageously, thesymmetries of the cut surface F are considered. It is also advantageousto take into account invariance of the angle imaging in the contactpressure transformation (angle about the optical axis) when choosing thepoints.

2. An interpolation surface I′ is adapted to the transformed pointsf_(i)′. Preferably, it is ensured that the symmetry properties of thesurface I′ deviate only slightly, if at all, from the cut surface F inthe non-transformed system.

3. It is further advantageous to adapt the interpolation surface I′ tothe transformed characteristic points f_(i)′ such that one of theparameters describing the surface is the height z or a parameter whichis a substitute in a known relationship to the height z, for which thusa representation such as for example I′:=r(z,φ) or I′:=y(z,x) applies.It is thereby easier to find a path curve for the target points whichcan be worked along as quickly as possible.

FIG. 11 shows a graphic illustration of the first method for a specificangle about the z axis. FIG. 11 shows by way of example a sectionalrepresentation through a correction surface F in the coordinates z andr. The angle φ of the cylinder coordinates corresponds to a rotation ofthe r axis about the z axis. Points f_(i) are then selected for thesurface F as characteristic points which are then transformed intopoints f_(i)′ with the contact pressure transformation AT. Theinterpolation surface I′ is then defined by the transformed pointsf_(i)′. This interpolation surface I′ then serves to determine thecontrol data.

However, the concept of the characteristic points f_(i) can also be usedin a simplified variant. In this case, the information on changing thesurface F→F′ is no longer transferred in full in the contact pressuretransformation AT. Instead, a suitable approximation surface Nwhich issubjected to the transformation AT is selected in the transformed system(contact glass system). Characteristic points f_(i) are again selectedfor the approximation surface and converted into transformed pointsf_(i)′ with the contact pressure transformation AT. An interpolationsurface I′ which connects (or approximates) the transformed pointsf_(i)′ is then again found by interpolation (if required byapproximation).

The deviation between the actual correction surface F and theapproximation surface Nis also taken into account. To do so, thedeviation D between the surfaces F and Nis determined in theuntransformed system. This deviation D can be determined in differentways. Firstly, it is possible to determine the deviation D for allcharacteristic points f_(i). There is then a set of deviation valuescorresponding to the set of characteristic points. Alternatively, it ispossible to determine a deviation function D.

The deviation D is then used to correct the interpolation surface I′.Either the interpolation surface I′ is corrected with it after theinterpolation or the transformed characteristic points f_(i)′ arecorrected with the deviation D and the interpolation surface I thendetermined. The latter is expedient when a set of deviation parametersis fixed for the set of characteristic points. Thus the followingfeatures are provided or possible:

1. The information about the cut surface F in the natural system isreduced by determining the approximation surface N. This is carried outby determining the approximation surface N for the cut surface F, forexample a sphere or a Zernicke polynomial with a reduced order comparedwith the cut surface.

2. Characteristic points f_(i) are determined for N. Advantageouslysymmetries of the surface N are considered. It is also advantageous totake into account invariances of the angle imaging in the contactpressure transformation (angle about the optical axis) when choosing thepoints.

3. The deviation D of the cut surface F from the approximation surface Nin the natural system (eye system) is determined.

4. The points f_(i) are transformed into f_(i)′ and the interpolationsurface I′ determined.

5. The symmetry properties of the interpolation surface I′ then deviateonly slightly from the approximation surface N in the untransformedsystem.

6. In order to transform the cut surface F as good as possible, thedeviation D is applied to I′, so that a function results which is a goodrepresentative of a transformed version of cut surface F.

7. The deviation D can be applied both to the interpolation surface I′an to the transformed pointsf', as already mentioned.

8. It is advantageous to adapt the interpolation surface I′ to thetransformed characteristic points f_(i)′ such that one of the parametersof the function is the height z. Naturally, a substitute in a knownrelationship thereto can also be used. The same applies to the deviationD.

The use of pulsed laser radiation is not the only way in which surgicalrefraction correction can be carried out. The determination, describedhere, of control data for operating the device can be used for almostany operating procedure in which, by means of a device, with control bycontrol data, a volume is removed from the cornea or added to it, asalready explained in the general section of the description.

Various embodiments of systems, devices, and methods have been describedherein. These embodiments are given only by way of example and are notintended to limit the scope of the claimed inventions. It should beappreciated, moreover, that the various features of the embodiments thathave been described may be combined in various ways to produce numerousadditional embodiments. Moreover, while various materials, dimensions,shapes, configurations and locations, etc. have been described for usewith disclosed embodiments, others besides those disclosed may beutilized without exceeding the scope of the claimed inventions.

Persons of ordinary skill in the relevant arts will recognize that thesubject matter hereof may comprise fewer features than illustrated inany individual embodiment described above. The embodiments describedherein are not meant to be an exhaustive presentation of the ways inwhich the various features of the subject matter hereof may be combined.Accordingly, the embodiments are not mutually exclusive combinations offeatures; rather, the various embodiments can comprise a combination ofdifferent individual features selected from different individualembodiments, as understood by persons of ordinary skill in the art.Moreover, elements described with respect to one embodiment can beimplemented in other embodiments even when not described in suchembodiments unless otherwise noted.

Although a dependent claim may refer in the claims to a specificcombination with one or more other claims, other embodiments can alsoinclude a combination of the dependent claim with the subject matter ofeach other dependent claim or a combination of one or more features withother dependent or independent claims. Such combinations are proposedherein unless it is stated that a specific combination is not intended.

Any incorporation by reference of documents above is limited such thatno subject matter is incorporated that is contrary to the explicitdisclosure herein. Any incorporation by reference of documents above isfurther limited such that no claims included in the documents areincorporated by reference herein. Any incorporation by reference ofdocuments above is yet further limited such that any definitionsprovided in the documents are not incorporated by reference hereinunless expressly included herein.

For purposes of interpreting the claims, it is expressly intended thatthe provisions of 35 U.S.C. § 112(f) are not to be invoked unless thespecific terms “means for” or “step for” are recited in a claim.

1. (canceled)
 2. A method for surgical correction of defective vision ofan eye of a patient, the method comprising: changing a curvature of acornea of the eye by generating a cut in the cornea by irradiating laserradiation into the cornea, wherein the cut circumscribes and isolates avolume of cornea tissue within in the interior of the cornea, andremoving the isolated volume of cornea tissue from within the cornea,making the cut circumscribing and isolating the volume to comprise ananterior and a posterior part, the anterior part lying at a constantdistance from a cornea front surface, and wherein the curvature of thecornea of the eye is changed by removal of the volume differently for atleast two radii, r1 and r2, around an optical axis.
 3. The methodaccording to claim 2, further comprising changing the curvature of thecornea of the eye by removal of the volume such that near vision iscorrected in a central area about the optical axis, defined by a radiusof a phototopic pupil and that a distant vision is corrected in a zonehaving greater diameters.
 4. The method according to claim 2, furthercomprising correcting near vision for a viewing distance between 25 cmand 70 cm.
 5. The method according to claim 2, further comprising makingr1 the radius of a phototopic pupil and making r2 larger than r1.
 6. Themethod according to claim 2, further comprising making r1 the radius ofa scotopic pupil and making r2 larger than r1.
 7. The method accordingto claim 2, further comprising changing the curvature of the cornea ofthe eye by removal of the volume to have a constant curvature in a zonebetween the radius of a phototopic pupil and the radius of a scotopicpupil, and positioning each radius around the optical axis.
 8. Themethod according to claim 2, further comprising modifying an opticalrefraction power of the cornea by changing the curvature of cornea andlocally varying a curvature radius of the cornea according toR_(CV)*(r,φ)=1/((1/R_(CV)(r,φ))+B_(COR)(r,φ)/(n_(c)-1))+F, whereinR_(CV)(r,φ) is a local curvature radius of the cornea before the volumeis removed, R_(CV)*(r,φ) is a local curvature radius of the cornea atremoved volume, n_(c) is a refractive index of the material of thecornea and F is a coefficient, and B_(COR)(r,φ) is a local change inoptical refraction power in a plane lying in the vertex of the corneaand required for correction of defective vision.
 9. The method accordingto claim 2, further comprising making a curvature radius of the corneapiecewise constant, but changing at a characteristic radius r_(ch)around the optical axis.
 10. The method according to claim 2, furthercomprising making a curvature radius of the cornea change continuouslyin a transition area between two radii around the optical axis.
 11. Themethod according to claim 2, further comprising making a curvatureradius of the cornea depend onan angle of rotation around the opticalaxis.
 12. A system for surgical correction of defective vision of an eyeof a patient, the system comprising: a laser treatment device configuredby control data to generate a cut within a cornea of the eye byirradiation laser radiation into the eye, and a planning stationconfigured to generate the control data, wherein the planning stationgenerates the control data to be adapted to control the laser treatmentdevice to generate the cut to circumscribe and isolate a volume ofcornea tissue within in the interior of the cornea, the removal of theisolated volume of cornea tissue from within the cornea changing acurvature of a cornea of the eye, and wherein the planning stationdefines the cut to comprise an anterior and a posterior part, theanterior part lying at a constant distance from a cornea front surface,and further defines the cut to circumscribe and isolate the volume suchthat removal of the volume changes a curvature of the cornea of the eyedifferently for at least two radii, r1 and r2, around an optical axis ofthe eye.
 13. The system according to claim 12, wherein the planningstation defines the cut to circumscribe and isolate the volume such thatremoval of the volume changes the curvature of the cornea of the eyesuch that near vision is corrected in a central area about the opticalaxis, defined by a radius of a phototopic pupil and that a distantvision is corrected in a zone having greater diameter.
 14. The systemaccording to claim 13, wherein the planning station defines the cut tocircumscribe and isolate the volume such that removal of the volumecorrects near vision for a viewing distance between 25 cm and 70 cm. 15.The system according to claim 12, wherein r1 is the radius of aphototopic pupil and r2 is larger than r1.
 16. The system according toclaim 12, wherein r1 is the radius of a scotopic pupil and r2 is largerthan r1.
 17. The system according to claim 12, wherein the planningstation defines the cut to circumscribe and isolate the volume such thatremoval of the volume changes the curvature of the cornea of the eye tohave a constant curvature in a zone between the radius of a phototopicpupil and the radius of a scotopic pupil, each radius around the opticalaxis.
 18. The system according to claim 12, wherein the planning stationdefines the cut to circumscribe and isolate the volume such that removalof the volume to modify an optical refraction power of the cornea bychanging the curvature of cornea and to locally vary a curvature radiusof the cornea of the according toR_(CV)*(r,φ)=1/((1/R_(CV)(r,φ))+B_(COR)(r,φ)/(n_(c)-1))+F, whereinR_(CV)(r,φ) is a local curvature radius of of the cornea before thevolume is removed, R_(CV)*(r,φ) is a local curvature radius of thecornea at removed volume, n_(c) is a refractive index of the material ofthe cornea and F is a coefficient, and B_(COR)(r,φ) is a local change inoptical refraction power in a plane lying in the vertex of the corneaand required for correction of defective vision.
 19. The systemaccording to claim 12, wherein a curvature radius of the cornea ispiecewise constant, but changes at a characteristic radius r_(ch) aroundthe optical axis.
 20. The system according to claim 12, wherein acurvature radius of the cornea changes continuously in a transition areabetween two radii around the optical axis.
 21. The system according toclaim 12, wherein a curvature radius of the cornea depends from an angleof rotation around the optical axis.
 22. The system according to claim12, further comprising a control unit operably coupled to the lasertreatment device and configured to control operation of the lasertreatment device according to the control data.
 23. The system accordingto claim 22, wherein the control unit is part of the planning station.